Sorry, I can't tell you anything about timbren axles except they cost much more than a tube axel with springs.
As to matching tires; I have 4 trailers, none have "matching" tires to any of my tow vehicles. Not sure what all my tires sizes are but none are even close to 37", right now none are even an "AT" tire. Your bike trailer is about the size of my tilt bed trailer (originally made for a riding lawn mower) or my TBT.
My enclosed trailer (ET) is 14x6x6.5, it tows my trike and is being modified for camping/mild overlanding.
As to "matching" tires, I'm considering putting 265 BFG KO2's on three wheels, 2 on a trailer and a spare, depending on conditions I'll swap wheels between the TBT and the ET. May consider that if you get another trailer behind that 3500.
A larger tire, even monster 37's wouldn't be a hill for your tow vehicle, after you're rolling you probably wouldn't know that trailer was hooked up. Even taking off from a stop light you'll forget it's back there with your rig. I doubt you'll even notice a difference in your MPG, but it won't help.
Advantages of large matching tires to a tow vehicle are obvious, but do you need them? No, I'd think it's a nice to have and far from a must have, so long as you have spares. Now that depends on your intended use (an answer I see often on this site), taller tires will increase ground clearance, so I would think that having your trailer frame at or near the height of your tow frame would be optimal. And, everyone knows taller tires will increase the approach and departure angles.
I'd say there are hundreds of threads here about tires, comments from those who know much more about them I do. What I do know is that bigger is not always better, that tires and wheels play on the suspension, it can get pretty expensive. As long as your trailer tires track in the same rut as your tow vehicle, the closer the better, you should be good, the tires don't have to be the same size as the tow vehicle, but it's nice if they are obviously.
Enclosed or flatbed, which is better? Same answer, it depends. Intended use? Not defining my use is how I ended up with 4 trailers!
OK, one is a 26' boat trailer, can't help that. Had I built my TBT a bit larger I wouldn't have needed the ET to haul the trike;
But, an ET protects the cargo, can be used as a hard sided camper (like in bear country).
An ET provides security for cargo, a tarp only hides it. (and, I would not put a tarp on my trike!)
An ET can carry more stuff, not in weight but more items, you can pack it to the ceiling if you stay safe with the weight and loading.
An ET can be weather tight, cargo will be dry and clean, if it is insulated you can keep cargo warm or even cool for the dog.
Down sides; an ET can only carry what fits trough the door(s)/ramp. While tear drops are cool, they are very limited.
So, size matters, it's not a good thing to tow a load wider than your tow vehicle, while you can go taller there are a few issues.
Sidewinds on a highway can wag the dog, the stronger the wind the less fun you'll have with an ET.
If the ET isn't really in the slip stream of your tow vehicle, headwinds will slow you down and your MPG will drop.
I've had flat front cargo trailers and a "V" nose has better stability down the highway, reduces the effects of headwinds and even a bit of sidewinds.
An ET can be an "eye sore" in some neighborhoods, they are more visible than a flatbed of equal size, so consider where to store it.
If your ET is tall enough to walk in and have greater utility but, your rear visibility behind your trailer is gone. You might need towing mirrors
and a review camera is on my list of trailer mods.
Now, many of these wind and visibility issues will apply to a flatbed with a heavy tarp, depending on the height of that covered load, as it becomes a sail.
As to build quality, got no idea how you drive! If you go blazing down a rough road in that 3500, if you don't tear up a trailer your cargo might get trashed.
All my trailers are steel, they are almost bullet proof (depending on the caliber). I wish my ET was aluminum, but it's durable.
You mentioned enclosing your trailer, I would if I were you, so the build quality is up to you.
The 2 big advantages of an ET are security and being weather tight, that alone is worth the build, IMO.
All the best! OMGY clear....
